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Quiz #1
1.5 hours  open books and notes
Problem 1
(25 points)
A device has a sensor connected to an alarming system. The sensor triggers with
probability 0.95 if dangerous conditions exist in a given day and with probability 0.005 if
conditions are normal during the day. Days with dangerous conditions occur with
probability 0.005. Given the above:
(a) What is the probability of false alarm, i.e. the probability that conditions are
normal when the alarm system triggers?
(b) What is the probability of unidentified critical condition, i.e. the probability that
conditions are dangerous when the system does not trigger?
(c) How many false alarms and how many unidentified critical conditions should be
expected to occur during a 10year period? Comment on the effectiveness of the
alarming system.
Problem 2
(25 points)
At a given site, floodproducing storms occur with mean rate
λ
= 1/(20 years).
(a) Considering the three conditions under which a point process is Poisson, state
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 Spring '05
 DanieleVeneziano

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